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%I #17 Jul 25 2021 13:55:08
%S 11,25,54,114,237,486,988,1998,4027,8097,16253,32587,65286,130727,
%T 261668,523631,1047669,2095900,4192576,8386223,16773924,33549888,
%U 67102592,134209071,268423507,536854419,1073719059,2147452226
%N a(n) is the number of binary strings of length n+3 such that there exists a subsequence of length 4 with 2 ones in it.
%C a(n) = 2^(n+4) - sum of all elements of the n-th power of the matrix [[1 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] [1 1 0 0 0]] which is the transition matrix for the last four bits being 0000, 0001, 0010, 0100, 1000. - _Joshua Zucker_, Aug 04 2006
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,1,-2).
%F G.f.: -x^4*(-11+8*x-x^2-2*x^3+8*x^4) / ( (2*x-1)*(x^4+x-1) ). - _R. J. Mathar_, Nov 28 2011
%t LinearRecurrence[{3,-2,0,1,-2},{11,25,54,114,237},30] (* _Harvey P. Dale_, Aug 14 2019 *)
%K nonn
%O 4,1
%A _Tanya Khovanova_, May 10 2006